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If the length, breadth and height of a cuboid is increased by 10%, 20%, 30% respectively. Then find the percentage increase in the volume of the cuboid?
- a)71.6%
- b)60%
- c)171.6%
- d)Can’t be determined
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If the length, breadth and height of a cuboid is increased by 10%, 20%...
Initial volume = l × b × h.
Increased volume will be equal to 1.1l ×1.2b ×1.3h = 1.716lbh.
Therefore, percentage increase in volume will be given by the expression
((1.716 - 1) ×lbh)/lbh×100 =71.6%
Most Upvoted Answer
If the length, breadth and height of a cuboid is increased by 10%, 20%...
To find the percentage increase in the volume of the cuboid, we need to compare the initial volume with the final volume after the dimensions have been increased.
Let's assume the initial length, breadth, and height of the cuboid are L, B, and H respectively.
Given that the length, breadth, and height are increased by 10%, 20%, and 30% respectively, the new dimensions of the cuboid will be:
New length = L + 10% of L = L + 0.1L = 1.1L
New breadth = B + 20% of B = B + 0.2B = 1.2B
New height = H + 30% of H = H + 0.3H = 1.3H
The initial volume of the cuboid is given by:
Initial volume = L*B*H
The final volume of the cuboid is given by:
Final volume = (1.1L)*(1.2B)*(1.3H)
To find the percentage increase in volume, we can use the formula:
Percentage increase = (Final volume - Initial volume) / Initial volume * 100
Substituting the values:
Percentage increase = [(1.1L)*(1.2B)*(1.3H) - L*B*H] / L*B*H * 100
Simplifying the expression:
Percentage increase = [(1.1*1.2*1.3) - 1] * 100
Percentage increase = (1.716 - 1) * 100
Percentage increase = 0.716 * 100
Percentage increase = 71.6%
Therefore, the percentage increase in the volume of the cuboid is 71.6% (option A).
Let's assume the initial length, breadth, and height of the cuboid are L, B, and H respectively.
Given that the length, breadth, and height are increased by 10%, 20%, and 30% respectively, the new dimensions of the cuboid will be:
New length = L + 10% of L = L + 0.1L = 1.1L
New breadth = B + 20% of B = B + 0.2B = 1.2B
New height = H + 30% of H = H + 0.3H = 1.3H
The initial volume of the cuboid is given by:
Initial volume = L*B*H
The final volume of the cuboid is given by:
Final volume = (1.1L)*(1.2B)*(1.3H)
To find the percentage increase in volume, we can use the formula:
Percentage increase = (Final volume - Initial volume) / Initial volume * 100
Substituting the values:
Percentage increase = [(1.1L)*(1.2B)*(1.3H) - L*B*H] / L*B*H * 100
Simplifying the expression:
Percentage increase = [(1.1*1.2*1.3) - 1] * 100
Percentage increase = (1.716 - 1) * 100
Percentage increase = 0.716 * 100
Percentage increase = 71.6%
Therefore, the percentage increase in the volume of the cuboid is 71.6% (option A).
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If the length, breadth and height of a cuboid is increased by 10%, 20%, 30% respectively. Then find the percentage increase in the volume of the cuboid?a)71.6%b)60%c)171.6%d)Cant be determinede)None of theseCorrect answer is option 'A'. Can you explain this answer?
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